In 1924, Louis de Broglie, as part of his PhD thesis, reworked Compton's momentum phenomena from the reverse direction; that is, he hypothesized that matter, in particular, electrons, could exhibit wave properties. These waves are now called matter waves.

p = h / λλdeBroglie = h / mv

De Broglie's matter waves proved to be the justification for Bohr's assumption that electrons maintained stable orbitals at special designated radii and did not spiral into the nucleus because they had quantized angular momentum. In 1929 de Broglie was awarded the Nobel Prize in Physics for his discovery of the wave nature of electrons.

The radius of a ground state, n = 1, electron has a circumference of one standing wave. The radius of the first excited state, n = 2, has a circumference of two standing waves. Thus, an electron's orbit cannot decay because it is constrained by its standing wave forms. Only those radii whose circumferences equaled a multiple of the electron's de Broglie wavelength were permitted.

De Broglie's matter waves were experimentally substantiated by the work of Davisson and Germer when they observed that streams of electrons, after passing through a graphite crystal, produced a diffraction pattern similar to that produced when a beam of x-rays passed through the same crystal.